Mathematical Modelling of the Effects of Health Interventions on the Evolution of Life History in Disease-Causing Organisms

Abstract

We use mathematical models to explore the evolutionary implications of health interventions affecting age-dependent mortality schedules in two contexts, antihelminthics targeting parasitic nematodes, and programs directed against malaria vectors. We show that interventions targeting parasitic nematodes can exert selection pressure to either shorten or extend the time to maturity, depending on the details of worm mortality functions with and without the intervention. Interventions may therefore generate selection favouring later-maturing, larger and more fecund worms, rather than inevitably favouring the evolution of smaller, less fecund and hence potentially clinically less damaging worms as previously assumed. The evolution of insecticide-resistant mosquitoes threatens conventional public health programs targeting malaria vectors. By exploiting the high mortality rates of wild mosquitoes and the delay between malaria infection and infectiousness in mosquito hosts, late-life-acting (LLA) insecticides which kill only older mosquitoes can in principle provide effective transmission control in combination with very low selection for resistance. We develop a novel mathematical model to evaluate the potential of such pesticides and find that theoretical LLAs which affect only mosquitoes above a specific age can offer transmission control comparable with conventional insecticides, combined with very low selection for resistance. Benefits are maximised by generating lower mortality in mosquitoes not infected with malaria, and contacting and killing mosquitoes prior to biting. We also explore the optimum virulence characteristics for a fungal LLA biopesticide, and find that it may offer improved transmission reduction as well as lower selection for resistance when compared to some insecticides in current use. Lastly we use our model to assess a candidate for development as a chemical LLA. Finally, we explore a disparity between our model results and the conventional wisdom that a rare, recessive resistance allele will not spread. We find that the assumption of discrete, non-overlapping generations is key in this context